9
1st Internatio nal Elec tro nic Conference o n Actuato r Technology: Materials, Devices and Applic atio ns (IeCAT 2020) Conference Proceedings Paper Design of electromechanical actuators for large sized valves Tobias Vonderbank 1,* , Katharina Schmitz 1 1 Institute for Fluid Power Drives and Systems (ifas), RWTH Aachen University * Correspondence: [email protected]; Tel.: +49 241 80-47722 Abstract: Increased performance in modern hydraulics is achieved by crucial investigation of pos- sible enhancements of its components. Previous research has pointed out that electromechanical actuators can represent an alternative to hydraulic pilot control systems. Since an additional pilot circuit is complex and expensive, there are advantages, especially for systems which currently rely on a separate hydraulic pilot circuit. Actuators for large sized valves have to meet various require- ments, such as applying high forces over large strokes. A functional structure of the “valve and its actuation system” has been derived to define these requirements effectively in order to develop an innovative valve actuator. The general function of the system is divided into elementary functions using this design method. Besides common actuators consisting of a switch and an energy converter, even more alternative actuator designs were pointed out by the comprehensive analysis of the func- tional structure. Since every actuator needs to be attached on any regular hydraulic valve, the de- signed actuator is presented and the most significant construction details are explained. In conclu- sion, this paper summarizes significant steps during the design process of alternative electrome- chanical actuators of hydraulic valves. It is intended to serve as a basis for the further development of innovative valve actuators. Keywords: Large sized valves, Electromechanical valve actuator, Spool resistance forces, Switching process, energy-efficient actuator 1. Introduction In modern hydraulic systems, large sized control valves are normally operated via smaller pilot valves. This type of actuation is characterized by very high realizable forces and large possible strokes. If the minimum working pressure of approximate 4 bar is not ensured during the switching process of the main valve, the resulting force is insufficient to switch the valve [1]. Therefore the pilot valve cannot be internally supplied [1]. In this case, the pilot valve has to be externally supplied. This requires a separate hydraulic circuit, which is normally operated as a constant pressure system [1]. New electromechanical actuators can be developed to replace the external pilot circuit, therefore en- hancing the hydraulic system. The requirements, which need to be fulfilled by the actuation system, strongly depend on the hydraulic system. Therefore, each design of a new valve actuator needs to be adapted to the considered system to achieve the most suitable solution. The presented paper is in- tended to give an overview over the design process of new electromechanical valve actuators. This paper is focused on the common definition of the requirements based on acting forces, as well as on the identification of innovative optimization potential. Therefore, the holistic system of the valve and its actuation system is investigated using the design method of functional structures explained in VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of

Design of electromechanical actuators for large sized valves · VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of . 1st International

  • Upload
    others

  • View
    5

  • Download
    2

Embed Size (px)

Citation preview

Page 1: Design of electromechanical actuators for large sized valves · VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of . 1st International

1st International Electronic Conference on Actuator Technology: Materials, Devices and Applications (IeCAT 2020)

Conference Proceedings Paper

Design of electromechanical actuators for large sized

valves

Tobias Vonderbank 1,*, Katharina Schmitz 1

1 Institute for Fluid Power Drives and Systems (ifas), RWTH Aachen University

* Correspondence: [email protected]; Tel.: +49 241 80-47722

Abstract: Increased performance in modern hydraulics is achieved by crucial investigation of pos-

sible enhancements of its components. Previous research has pointed out that electromechanical

actuators can represent an alternative to hydraulic pilot control systems. Since an additional pilot

circuit is complex and expensive, there are advantages, especially for systems which currently rely

on a separate hydraulic pilot circuit. Actuators for large sized valves have to meet various require-

ments, such as applying high forces over large strokes. A functional structure of the “valve and its

actuation system” has been derived to define these requirements effectively in order to develop an

innovative valve actuator. The general function of the system is divided into elementary functions

using this design method. Besides common actuators consisting of a switch and an energy converter,

even more alternative actuator designs were pointed out by the comprehensive analysis of the func-

tional structure. Since every actuator needs to be attached on any regular hydraulic valve, the de-

signed actuator is presented and the most significant construction details are explained. In conclu-

sion, this paper summarizes significant steps during the design process of alternative electrome-

chanical actuators of hydraulic valves. It is intended to serve as a basis for the further development

of innovative valve actuators.

Keywords: Large sized valves, Electromechanical valve actuator, Spool resistance forces, Switching

process, energy-efficient actuator

1. Introduction

In modern hydraulic systems, large sized control valves are normally operated via smaller pilot

valves. This type of actuation is characterized by very high realizable forces and large possible

strokes. If the minimum working pressure of approximate 4 bar is not ensured during the switching

process of the main valve, the resulting force is insufficient to switch the valve [1]. Therefore the pilot

valve cannot be internally supplied [1]. In this case, the pilot valve has to be externally supplied. This

requires a separate hydraulic circuit, which is normally operated as a constant pressure system [1].

New electromechanical actuators can be developed to replace the external pilot circuit, therefore en-

hancing the hydraulic system. The requirements, which need to be fulfilled by the actuation system,

strongly depend on the hydraulic system. Therefore, each design of a new valve actuator needs to be

adapted to the considered system to achieve the most suitable solution. The presented paper is in-

tended to give an overview over the design process of new electromechanical valve actuators. This

paper is focused on the common definition of the requirements based on acting forces, as well as on

the identification of innovative optimization potential. Therefore, the holistic system of the valve and

its actuation system is investigated using the design method of functional structures explained in

VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of

Page 2: Design of electromechanical actuators for large sized valves · VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of . 1st International

1st International Electronic Conference on Actuator Technology: Materials, Devices and Applications (IeCAT 2020)

2

innovative valve actuators is shown, while the graphical representation is extended by further ele-

mentary functions. More innovative valve actuators, considering the whole system of the valve and

its actuation system, are taken into account by this extended functional structure.

Based on a presented electromechanical actuator it is explained which further features need to

be considered during the design process. Further forces, which are applied by the implementation of

an electromechanical actuator are evaluated through carried out measurements. It is explained how

these can be held negligible small.

2. Elementary function of a directional control valve

Using the design method of functional structures, the general function of a technical system is

divided consequently into elementary functions. In presented paper the displayed symbols according

to table 1 are used to represent them. The general function is divided until a functional structure

sufficient for the aimed design process is obtained.

Table 1. Symbols of elementary functions in accordance with [4].

separate/connect mate-

rial flow

energy flow

link/divide material

flow

material flow

reduce/increase energy

of material flow

information flow

link/divide energy flow

store energy

separate/connect energy

flow

subsystem

convert energy flow

not further specified

hydraulic system

According to BACKÉ , the general function of a control valve can be formulated as: “Open-

ing/Closing of different flow paths” [5]. Since the hydraulic system often is embedded into a higher-

level control system the main function can be extended to “Opening/Closing of different flow paths

according to an electrical control signal”. In the first step this main function can be divided into two

main functions, namely “Conduction of hydraulic energy depending on the position” and “Position-

ing of the spool according to an electric signal”, as shown in Figure 1.

Figure 1. Splitting of the general function.

Whereby the conduction of hydraulic energy is realized by the geometry of the spool and its

positioning by the actuation system of the valve. Since the positioning of the spool is realized by a

controlled force application the function can be reformulated to “Applying force to the spool accord-

ing to an electric signal”.

Opening/Closing of different flow paths

according to an electric control signal

Conduction of hydraulic energy

depending on the position

Positioning of the spool

according to an electric signal

Page 3: Design of electromechanical actuators for large sized valves · VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of . 1st International

1st International Electronic Conference on Actuator Technology: Materials, Devices and Applications (IeCAT 2020)

3

3. Design of new valve actuation systems

Actuators need to overcome all forces opposing the movement or tending to close the valve to

ensure the general function. Forces acting on the spool of a pilot operated 4/3 directional control valve

are shown in Figure 2.

Figure 2 Forces at the spool with accordance to [6, 7.]

In addition to friction forces FFriction and inertia forces FInertia, the actuator also needs to overcome

the spring forces FSpring and the flow forces FFlow, which normally act in closing direction [6, 8]. The

spring forces must be high enough, so that the valve is able to close at any given operation condi-

tion [6, 8]. A preload on the spring prevents the spool from overshooting [6, 8]. The flow force mostly

represents the most significant resistance of these forces [9]. Also, an additional inherent force FPressure

is caused by the fluid in the passive pilot chamber, as is the case of a pilot operated valve. Fluid is

displaced by the movement of spool. A pressure rise in the passive pilot chamber can occur depend-

ing on the hydraulic resistance of the drain line.

Functional structure of a pilot operated large sized valve

A functional structure of a 4/3 directional control valve has been derived in Figure 3 based on

the two main functions of a directional control valve according to Figure 1. The notation of elemen-

tary functions according to Table 1 is used in following figure.

Figure 3. Functional structure of a valve and its actuation system.

Movement

direction

FFriction

FInertia

FFlow

FSpring

FPressure P A T T B

Page 4: Design of electromechanical actuators for large sized valves · VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of . 1st International

1st International Electronic Conference on Actuator Technology: Materials, Devices and Applications (IeCAT 2020)

4

The functional structure can be divided into different subsystems. Subsystem 1) represents the

functions attributed to the spool geometry. The flow rate which is entering the system through port

P is conducted by the metering edges a) to the working ports of the valve. During the flow conduction

a part of the energy is transformed into mechanical energy b), which acts as flow force on the spool.

This force normally tends to close the valve. Leaving the subsystem 1), the fluid enters a not further

specified hydraulic system. Fluid flows back into the tank resulting in additional flow forces

During the positioning of the spool the actuation unit needs to apply a force larger than all re-

sistance forces acting on the spool. As shown in Figure 2, these consist of flow forces FFlow, friction

forces FFriction, inertia forces FInerta, spring forces FSpring and forces resulting of the hydraulic resistance

of the drain line of the passive pilot chamber FPressure. Most of these forces are shown leaving the func-

tional structure, since they represent dissipation (friction, inertia and further resistance forces). Flow

forces are applied in the valve and are acting on the spool, therefor e displayed on the functional

structure as generated forces, which are subtracted from the actuation system force. The remaining

force acts against the centering spring, while the spool is deflected into its working position.

The mechanical energy is stored in the spring c), as long as the actuation system provides suffi-

cient force. If the actuation force is reduced, the stored energy is released, thus centering the spool.

The stored energy is, according to the spring stiffness, a function of the stroke, which is why an in-

formation flow is drawn from the spring c) to the metering edges a).

The subsystem 2) needs to be analyzed in detail to design a direct electromechanical valve actu-

ation system. This subsystem consists at least out of two essential functions, as shown in Error! Ref-

erence source not found. . [10]

Figure 4. Minimal functional structure of an actuation system according to [10.]

Every actuator consists at least of a switch and an energy converter [10]. This can be a pilot

operation circuit where the pilot valve is the switch and the energy conversion is realized in the pilot

chamber. Focusing on the design of an electromechanical valve actuation system , the energy con-

verter is electromechanical, such as solenoids or electrical motor. An evaluation on electromechanical

converters was carried out to analyze their suitability for the given application. As a result, an elec-

trical motor followed by a mechanical component to convert rotary into translatory movement was

the optimal concept.

Designed electromechanical vavle actuation system

A prototype of an electromechanical valve actuator for hydraulic valves has been designed t o

identify the most critical and important construction details (Figure 4). It is based on a stepper motor

(1). The rotary energy is converted to a linear movement by a steep threaded rod (2) and the corre-

sponding nut (3). The model is equipped with necessary sensors for measurements of displacement

and force signals (4 and 5). Since it was designed for the control of a large sized directional control

valve of nominal size 25 in a flow-controlled system, forces up to 500 N are realizable with the actu-

ator.

Page 5: Design of electromechanical actuators for large sized valves · VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of . 1st International

1st International Electronic Conference on Actuator Technology: Materials, Devices and Applications (IeCAT 2020)

5

Figure 4. Designed electromechanical valve actuation system.

As seen in Figure 4 the designed electromechanical actuator is mounted outside the valve. This

makes it possible to apply to every common valve by adjusting the valve connector (6).

Design features of the electromechanical valve actuation system

Certain design features must be taken into account if the valve actuator is designed inde-

pendently from the valve. These result from the design of the valve and can cause additional un-

wanted forces if they are not considered properly. To highlight these features, a sectional view of a

regular pilot operated valve is shown in Figure 5. The spool of the valve is extended at both ends by

a rod, creating a mechanical connection to the outside of the valve. These connections are required as

the valve is switched electromechanically.

Figure 5. Special design features for an outside mounted electromechanical actuation system.

In the case of externally attached actuators, mechanical connectors are necessary to transmit ten-

sile and compressive forces required for the actuation of the valve. Actuators, which are able to in-

duce both forces are therefore attached only on one side of the valve. In this configuration, the spool

has to be balanced, taking into account the pressure forces at the front sides. To ensure that the pres-

sure in both sides is identical, the pilot chambers needs to be short circuited. Since the actuator design

is externally attached, an internal connection between both pilot chambers of the valve is not possible.

Sealing

2

3

1

5

4

6

Mechanical connection

QLeakage

Adapter plate

Page 6: Design of electromechanical actuators for large sized valves · VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of . 1st International

1st International Electronic Conference on Actuator Technology: Materials, Devices and Applications (IeCAT 2020)

6

Therefore, an adapter plate is mounted on the top of the valve instead of the pilot valve. As , the

mechanical connection reduces the pressurized area it should be implemented on both sides.

Short-circuiting both pilot chambers with each other has an additional effect. During the move-

ment of the spool, one chamber is expanded, whereas the other is contracted. Therefore, fluid must

be able to enter or exit the chambers. This action would require a compensation volume, but using

the adapter plate, the displaced volume in one chamber is compensated in the other, thus maintaining

a constant volume. No additional volume is necessary. Enabling the fluid to oscillate between the

chambers it needs to overcome the inherent resistance. Therefore, a small pressure difference between

the two chambers arises. This needs to be considered in the design of the electromechanical actuator.

To investigate this effect, the actuator was driven with different speeds and the required force was

measured. The results are shown in Error! Reference source not found. a). The necessary force to

move the spool at even tenfold the actuator speed does not increase significantly. It can therefore be

concluded that this influence is extremely small considering the other factors.

Additional sealings on the caps are necessary to avoid external leakage, leading to further fric-

tion forces to be overcome by the actuator. These forces strongly depend on the pressure in the pilot

chambers. Further measurements have been conducted to investigate this effect. The force require-

ments by different pressure levels in the pilot chamber is illustrated In Error! Reference source not

found. b).

(a)

(b)

Figure 7. a) Influence of actuator speed on applied forces b) Relation between pressure le vel and

friction forces.

As can be seen in the figure, this effect is not negligible. Even a chamber pressure of 10 bar leads

to a significant increase of the required actuator force. Therefore, the pressure in the pilot chambers

have to be reduced as much as possible. The pressure in the pilot chamber is adjusted to the pressure

at the T port of the valve since there is a leakage flow over the spool. Therefore, the maximum pres-

sure at the tank line of the valve must be considered during the design of outside attached actuators.

In case of systems where the pressure at the valve T port can reach high values an additional drain

line in the adapter plate will ensure low pressure in the pilot chamber. The aforementioned design

features are only valid for outside attached actuators, which are normally designed independently

from the valve geometry. The additional sealing, and therefore the draining line becomes redundant

with the development of an actuation system, which can be pressurized. The adapter plate becomes

unnecessary if a direct connection between both chambers is provided.

Innovative electromechanical valve actuation system

Page 7: Design of electromechanical actuators for large sized valves · VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of . 1st International

1st International Electronic Conference on Actuator Technology: Materials, Devices and Applications (IeCAT 2020)

7

The previously presented actuator is one possible solution while focusing on the functional

structure of an actuator. A holistic view of the functional structure of a “valve and its actuation sys-

tem” leads to further innovative solutions. In the following Error! Reference source not found. , the

functional structure of the “valve and its actuation system” was extended by two additional subsys-

tems {3) and 4)}.

Figure 8. Extended functional structure of “valve and its actuation system”.

Other than the additional subsystems, the functional structure is kept the same. Subsystem 1)

represents the valve and subsystem 2) the main actuator. New valve actuation systems can be derived

based on this functional structure, because the requirements of the individual actuators change by

combining various subsystems.

Solutions proposed by the subsystem 3) cover all actuation systems, which are extended by an

additional actuator 3) to keep the spool in position when it has reached the desired stroke. Therefore,

the main actuator (subsystem 2)) does not need to constantly apply the necessary force. The actuator

only needs to surpass the opposing forces for a short time. After that, the spool is held in position by

the actuator 3). It is conceivable for a design that the actuator 3) holds the spool in position by means

of clamping forces. In this case the actuator 3) only needs to realize relative small strokes. Due the

clamping movement can be realized orthogonal to the spool movement. One example where the

clamping idea is realized is a piezoelectric inchworm motor

Solutions resulting of subsystem 4) seem more promising. The general function of the springs is

to move the spool into a defined position. In the case of the here analyzed 4/3 directional control valve

it is the centered position. In the functional structure in Error! Reference source not found. the

springs are displayed as accumulators c). A closer look to the general function of the springs shows

that there are two relevant operations. On the one hand, the springs need to center the spool accord-

ing to the operation cycle, while one the other hand they need to center the spool in case of failure, as

in a power outage. Therefore, the general function can be divided into two different functions, ac-

cording to Error! Reference source not found. .

Figure 9. Divided general function of the springs.

Move the spool into a centered position

According to the operation cycle In case of power outage

Page 8: Design of electromechanical actuators for large sized valves · VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of . 1st International

1st International Electronic Conference on Actuator Technology: Materials, Devices and Applications (IeCAT 2020)

8

In common pilot operated valves, providing energy for the switching process and compressing

the springs takes place simultaneously. While moving the spool into the end position a part of the

actuator’s energy is used to compress the springs. This energy is stored in the springs and is required

for the reset process. The time dependency can be solved by the separation and redistribution of the

spring functions into further components. The first function can be covered by the main actuator

using a proportional actuator like the one present before. Therefore, the springs only must center the

spool in case of power outage. Thus, the energy stored in the springs only comes to effect in case of

an error. They remain compressed most of the time by the additional force of subsystem 4). The re-

quirements for the applied force of the switching actuator decrease as the high spring forces can be

temporarily removed during normal operation.

Two principal solutions turned out to be the most suitable. In one alternative, the springs are

preloaded by the main actuator while being held compressed by magnets. Since magnets are optimal

for applying high forces at zero gap, they comply perfectly the requirements for this function. During

an initial start of the system, the main actuator moves the spool in each end position to compress the

springs. This can be done with low velocity . Therefore, the necessary power is reduced. Reaching the

end position, the magnets are activated and ensure the holding of the compressed springs. Subse-

quently, the spool can be moved by the main actuator without applied spring forces. In case of power

failure, the magnets are deactivated, causing the springs to decompress and thus centering the spool.

This concept is ideal for an actuator , based on a stepper motor, since it can provide large torque dur-

ing a slow rotation speed. During further operation, the actuator does not need to work against the

spring forces anymore. Therefore, the necessary power is reduced drastically.

In another alternative solution an extra chamber containing the spring is designed to preload

these by application of hydraulic energy. Hydraulic fluid can be diverted from the main system dur-

ing high pressure phases, since the time dependency is solved. Thus avoiding an additional pilot

circuit. Hydraulic pressure controlled by two valves regulate the energy stored in the springs. The

first valve is placed to separate the spring chamber from the hydraulic main system, ensuring the

preload to remain even in phases of low pressure. The second valve ensures the pressure relief of the

spring chamber to the tank in case of a power outage. The missing hydraulic energy in the spring

chamber releases the stored energy in the springs, forcing them to expand and thereby centering the

spool. Since the springs are preloaded by another actuator during normal operation , the force re-

quirement in the electromechanical actuation system is reduced.

4. Discussion

During the design process of innovative electromechanical valve actuation system s, the func-

tional structure represents an important design method. Even if the investigation of the acting forces

is indispensable, the functional structure enables a holistic view over the valve and its actuation sys-

tem. This allows not only the design based on known forces, but also taking into account all other

components and other system-related aspects. Separation and redistribution of elementary functions

of different components enable further optimization not restricted to the reduction of flow forces.

This is an effective approach to reduce the requirements during the design process of valve actuation

systems, see for example [9, 11]. The functional structure derived in this paper leads to a solution

where the spring forces are compensated. Thus, reducing the requirements of the main actuator mas-

sively. This proposed solution can only be implemented in actuators which can switch the spool ac-

tively in the desired positions. The presented actuator also fulfills this requirement. Therefore an ex-

pansion and further investigation should be carried out, since it is a concept with broader potential.

Even if the functional structure may be extended further, the derived structure already contains some

significant correlations, which can help during the development of further valve actuator systems.

5. Conclusion

Page 9: Design of electromechanical actuators for large sized valves · VDI 2222 [2], PAHL/BEITZ [3] or KOLLER [4]. The potential of functional structures for the design of . 1st International

1st International Electronic Conference on Actuator Technology: Materials, Devices and Applications (IeCAT 2020)

9

In the presented paper the design process of a new electromechanical valve actuator for large

sized directional control valves is investigated. An innovative electromechanical valve actuation sys-

tem is generated focusing on the derivation of the functional structure and identification of special

design features. Measurements carried out on a prototype are investigated to evaluate special design

features which need to be considered during the design process. Effects in the pilot chamber must be

considered for outside mounted electromechanical actuators. Since additional sealings are necessary,

both pilot chambers are to be short-circuited and released against the tank to decrease the load on the

actuator, due to the sealing friction forces. Since the pilot chambers are expanded and contracted

during the movement short-circuiting is necessary to keep the total volume constant. Therefore, no

compensation volume is required.

The functional structure was extended aiming to point out further innovative solutions. These

consider the whole system of the valve and its actuation system. Proposing a solution, where the

designed electromechanical actuator is extended by magnets to keep the springs compressed, points

out how useful the functional structure can be.

Acknowledgments:

The IGF research project 20084N of the research association Forschungskuratorium Maschinenbau e. V. – FKM,

Lyoner Straße 18, 60528 Frankfurt am Main was supported from the budget of the Federal Ministry of Economic

Affairs through the AiF within the scope of a program to support industrial community research and develop-

ment (IGF) based on a decision of the German Bundestag.

Conflicts of Interest:

The authors declare no conflict of interest.

References

[1] G. Bauer, Ö lhydraulik: Grundlagen, Bauelemente, Anwendungen: Vieweg + Teubner, 2009.

[2] Konstruktionsmethodik, VDI 2222, 1997.

[3] J. Feldhusen and K.-H. Grote, Eds., Pahl/Beitz Konstruktionslehre: Methoden und Anwendung

erfolgreicher Produktentwicklung, 8th ed. Berlin, Heidelberg: Springer-Verlag GmbH, 2013.

[4] R. Koller and N. Kastrup, Prinziplösungen zur Konstruktion technischer Produkte: Springer -Verlag

GmbH, 2013.

[5] W. Backé and W. Hahmann, Grundlagen der Ö lhydraulik: Umdr. zur Vorlesung: Institut für hydraulische

und pneumatische Antriebe und Steuerungen der RWTH (IFAS), 1974.

[6] Helmut Tatar, Störkräfte bei elektromagnetisch betätigte Wegeventilen. Aachen, 1974.

[7] K. Schrank and H. Murrenhoff, “Beschreibung der Strömungskraft in Längsschieberventilen mittel

Impulserhaltung,” O+P Journal, no. 4, pp. 4–15, 2013.

[8] W. Backé and H. Tatar, Untersuchung des Einflusses von Störkräften auf den Schaltvorgang bei

Wegeventilen der Hydraulik. Opladen: Westdt. Verl., 1975.

[9] Christoph Latour, Strömungskraftkompensation von hydraulischen Sitzventilen. Aachen, 1996.

[10] H. Janocha, Unkonventionelle Aktoren: Eine Einführung. München: Oldenbourg Wissenschaftsverlag

GmbH, 2010.

[11] G. Schuster, CFD-gestützte Maßnahmen zur Reduktion von Strömungskraft und Kavitation am Beispiel

e ines hydraulischen Schaltventils. Aachen: Shaker, 2005.